I just read this post, and I do understand what the difference is. But still in my head I have the question. Can/Should I use it in the same App/Website? Say I want the AngularJs to fetch content and update my page, connecting to a REST api and all of that top stuff. But on top of that I also want a realtime chat, or to trigger events on other clients when there is an update or a message received.

Does Angular support that? Or I need to use something like Socket.io to trigger those events? Does it make sense to use both?
If someone could help me or point me to some good reading about that if there is a purpose for using both of them together.

As noted in the answer in your linked post, Angular does not currently have built-in support for Websockets. So, you would need to directly use the Websockets API, or use an additional library like Socket.io.

However, to answer your question of if you should use both a REST api and Websockets in a single Angular application, there is no reason you can't have both standard XmlHttpRequest requests for interacting with a REST api, using $http or another data layer library such as BreezeJS, for certain functionality included in various parts of the application and also use Wesockets for another part (e.g. real time chat).

Angular is designed to assist with handling this type of scenario. A typical solution to would be to create one or more controllers to handle the application functionality and update your page and then creating separate Services or Factories that encapsulate the data management of each of your data end points (i.e. the REST api and the realtime chat server), which are then injected into the Controllers.

There is a great deal of information available on using angular services/factories for managing data connections. If you're looking for a resource to help guide you on how to build an Angular application and where data services would fit in, I would recommend checking out John Papa's AngularJS Styleguide, which includes a section on Data Services.